On extremal finite packings (Q1849445)

For the classical infinite packing problems in \(E^2\) or \(E^3\) maximum density is attained by lattice packings. Here the author shows that for a large class of finite packing problems, even in 2 dimensions, which includes the maximum parametric density problem, the minimum perimeter problem, various container problems, and the minimum diameter problem, the extremum is not attained by a lattice packing, if the number of translates is sufficiently large (such answering a question of P. Erdős).